Let's take a look at the source code for Apple's ping implementation. Notably, we see this:

if (getuid())
    s = socket(AF_INET, SOCK_DGRAM, IPPROTO_ICMP);
else
    s = socket(AF_INET, SOCK_RAW, IPPROTO_ICMP);
sockerrno = errno;

getuid returns 0 if root. So this code is saying, "open the socket in DGRAM (datagram mode) if we are not root. If we are root, open as raw".

So a raw socket is only used when you are root. An IMCP ping packet is a standard DGRAM packet and does not require raw sockets.

However, there are some flags that can be passed to ping that do require root, and for those you will get an "Operation Not Permitted". For example:

>ping -f
ping: -f flag: Operation not permitted

When run as root, I do not get the operation not permitted. So Apple's implementation will let you do standard ping operations which does not require root, but require you to run as root for certain flags and operations.

Depending on if you are root, it may set some additional socket options:

if (uid == 0)
    (void)setsockopt(s, SOL_SOCKET, SO_SNDBUF, (char *)&hold,
        sizeof(hold));

Yes, after midnight, April 12, 2018 in the user's local time zone

From Ars Technica's "Apple has begun notifying macOS users of coming 32-bit app incompatibility".

Starting at midnight April 12, 2018 in the user's local time zone, they will see the following message the first time they launch an app that only supports 32-bit in macOS High Sierra 10.13.4:

This app needs to be updated by its developer to improve compatibility.

Along with that message, they'll see a "learn more" link that takes them to Apple's support page on the subject with more information. The support page broadly explains Apple's plans to "eventually" require all Mac software to be 64-bit.